Using recent progress in biological scaling, we explore the way in which the immune system of an animal scales with its mass (M). It is shown that the number of cells in a single clone of B cells should scale as M and that the B-cell repertoire scales as ln (cM), where c is a constant. The time that a B cell needs to circulate once through the organism is shown to scale as M(1/4)ln (cM). It is suggested that the scaling of other cell populations in the immune system could be derived from these scaling relations for B cells.